Joe Shipman wrote:
> Rejecting the idea that all properties/subsets are
> decidable/detatchable is not enough, because the particular property
> being discussed here, primeness, is a very concrete, ...
The property P(n) =
> "there is a pair of twin primes above n"
has not been decided. Is the statement P(10^(10^10)) determinate given
that the set of integers exists as a completed whole?
> "the set of integers exists as a completed whole" means, to
> me, that the set of integers is something you can quantify
> over with no loss of meaning.
(I am reminded, perhaps for no good reason, of a claim, that I never
quite understood, to the effect that "there exists a prime greater
than 10" is meaningless, or at least improper. I suppose the defect is
that the quantification is over the set of integers.)
Can't we understand the meaning of the statement P(10^(10^10)) without
claiming that it is determinate?
--Fred